ATOMOSYDhttp://www.atomosyd.net/
Analyse TOpologique et MOdélisation de SYstèmes Dynamiques. ATOMOSYD is an acronym to designate the approach we develop to investigate dynamical systems. We are concerned by the topological analysis, that is, a global approach of the phase portrait, and by the possibility to obtain a set of differential equations from measurements. Our researches are performed in CORIA which belongs to CNRS.frSPIP - www.spip.netATOMOSYDhttp://atomosyd.net/index.php/includes/xml/dist/images/IMG/siteon0.gifhttp://www.atomosyd.net/
802131987 A normal form for the Belousov-Zhabotinski reactionhttp://atomosyd.net/spip.php/overlib/spip.php?article202
http://atomosyd.net/spip.php/overlib/spip.php?article2022018-09-02T12:27:37Ztext/htmlfrLetellier3D flows
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The simple three-dimensional model <br />for describing the oscillations in the concentration of Ce ions was proposed by Françoise Argoul (University of Bordeaux) and co-workers. A numerical integration of this model (Fig. 1b) produces a chaotic attractor whose template contains the three branches which were identified in the experimental data. This model also captures the main characteristics of the experimental dynamics. When the parameter mu is varied, there is a period-doubling cascade (...)
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<a href="http://atomosyd.net/spip.php/overlib/spip.php?rubrique5" rel="directory">3D flows</a>
1978 : The Curry-Yorke maphttp://atomosyd.net/spip.php/overlib/spip.php?article201
http://atomosyd.net/spip.php/overlib/spip.php?article2012018-08-27T12:15:45Ztext/htmlfrLetellierDiscrete maps
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James H. Curry and James Yorke proposed in 1978 a two-dimensional map for a illustrating one of the routes to chaos from a quasi-periodic behavior. This map results from he composition of two simple homeomorphisms. The first homeomorphism is defined in polar coordinates by % <br />and the second is defined in Cartesian coordinates according to <br />The Curry-Yorke map is <br />The numerical invstigation starts with three typical behaviors solutions to the Curry-Yorke map, namely a quasi-periodic regime (...)
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<a href="http://atomosyd.net/spip.php/overlib/spip.php?rubrique7" rel="directory">Discrete maps</a>
A symbolic nonlinear theory for network observabilityhttp://atomosyd.net/spip.php/overlib/spip.php?article200
http://atomosyd.net/spip.php/overlib/spip.php?article2002018-05-25T11:36:54Ztext/htmlfrAGUIRRE, Letellier, SENDINA-NADALObservability of networks
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Work presented at NetSci 2018, Paris. <br />The observability of a complex system refers to the property of being able to infer its whole state by measuring the dynamics of a limited set of its variables. Since monitoring all the variables defining the system's state is experimentally infeasible or inefficient, it is of utmost importance to develop a methodological framework addressing the problem of targeting those variables yielding full observability. Despite several approaches have been (...)
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<a href="http://atomosyd.net/spip.php/overlib/spip.php?rubrique37" rel="directory">Observability of networks</a>
2018http://atomosyd.net/spip.php/overlib/spip.php?article198
http://atomosyd.net/spip.php/overlib/spip.php?article1982018-02-28T14:52:23Ztext/htmlfrPapers
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C. Letellier, I. Sendiña-Nadal, E. Bianco-Martinez & M. S. Baptista <br />A symbolic network-based nonlinear theory for dynamical systems observability <br />Scientific Reports, 8, 3785, 2018. <br />Abstract <br />When the state of the whole reaction network can be inferred by just measuring the dynamics of a limited set of nodes the system is said to be fully observable. However, as the number of all possible combinations of measured variables and time derivatives spanning the reconstructed state of the (...)
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<a href="http://atomosyd.net/spip.php/overlib/spip.php?rubrique13" rel="directory">Papers</a>
1987 The Ikeda delay differential equationhttp://atomosyd.net/spip.php/overlib/spip.php?article197
http://atomosyd.net/spip.php/overlib/spip.php?article1972018-01-06T17:22:52Ztext/htmlfrLetellierHigher dimensional flows
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Kensuke Ikeda proposed a model of a passive optical resonator system . When the system is an optical bistable resonator, Ikeda and Kenji Matsumoto showed that the dynamics can be reproduced with the single delay differential equation <br />For μ = 16 and x0 = π/3, δt = 0.002 and x(0)=2.5, the chaotic attractor shown in Fig. 1 is obtained. These parameter values were obtained by looking for a simple attractor starting from those provided by (...)
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<a href="http://atomosyd.net/spip.php/overlib/spip.php?rubrique6" rel="directory">Higher dimensional flows</a>
1984 A piecewise system for quasi-periodic and chaotic motionshttp://atomosyd.net/spip.php/overlib/spip.php?article196
http://atomosyd.net/spip.php/overlib/spip.php?article1962017-11-18T15:53:34Ztext/htmlfrLetellier3D flows
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When b=0, this system is conservative and produces quasi-periodic motions as evidenced in the Poincaré section defined by y=0 and shown in Fig. 1. Using x0 = 0.1417, y0=z0=0, there is most likely a weakly chaotic toroidal motion (shown in green in Fig. 1.).
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<a href="http://atomosyd.net/spip.php/overlib/spip.php?rubrique5" rel="directory">3D flows</a>
1974 : The Pylkin attractorhttp://atomosyd.net/spip.php/overlib/spip.php?article195
http://atomosyd.net/spip.php/overlib/spip.php?article1952017-11-06T20:00:51Ztext/htmlfrLetellierDiscrete maps
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A Plykin attractor is a limit set for a map defined - initially defined on a plane in the spirit of Smale's horseshoe by Romen Vasil'evich Plykin . As reported in , "Plykin also showed that the complement of a connected 1-dimensional basic set of the diffeomorphism of the 2-sphere consists of at least four connected components (the Plykin attractor has precisely four components in its complement), each containing at least one periodic attracting or repelling point. The Plykin (...)
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<a href="http://atomosyd.net/spip.php/overlib/spip.php?rubrique7" rel="directory">Discrete maps</a>
1986 The Nosé-Hoover system (Sprott A system)http://atomosyd.net/spip.php/overlib/spip.php?article193
http://atomosyd.net/spip.php/overlib/spip.php?article1932017-07-19T18:37:31Ztext/htmlfrLetellier3D flows
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Shūichi Nosé and by William Hoover , investigated a system of N particles (d degrees of freedom) in a given volume V and interacting (heat transfer) with an external system in such a way that the energy E is conserved. The equations governing the coordinates Q, the momentum P and the effective mass s, after a coordinate transformation, were <br />which were rediscovered by Julian Clinton Sprott as the Sprott A system. This system is a conservative system as shown by its Jacobian (...)
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<a href="http://atomosyd.net/spip.php/overlib/spip.php?rubrique5" rel="directory">3D flows</a>
2015 Deterministic approach of cancer dynamics : toward an individualization of pronostic for cancer evolutionhttp://atomosyd.net/spip.php/overlib/spip.php?article192
http://atomosyd.net/spip.php/overlib/spip.php?article1922017-04-28T14:52:36Ztext/htmlfrVIGERPh'D Thesis
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Abstract <br />Currently, most research in oncology involve genetic mutations potentially responsible for cancer initiation. Since the identification of a large number of genes involved in carcinogenesis is not correlated to an increase in number of patients in remission, investigating a cancer as a pure genetic process was not effecient as initially expected. Although genetic mutations have a key role in tumorigenesis, some other factors such as the micro-environment should be also (...)
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<a href="http://atomosyd.net/spip.php/overlib/spip.php?rubrique27" rel="directory">Ph'D Thesis</a>
2003 A simple model for spiking neuronshttp://atomosyd.net/spip.php/overlib/spip.php?article191
http://atomosyd.net/spip.php/overlib/spip.php?article1912017-04-16T03:28:43Ztext/htmlfrLetellierBiological models
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Eugene M. Izhikevich presented a model that reproduces spiking and bursting behavior of known types of cortical neurons . The model combines the biologically plausibility of the dynamics underlying the Hodgkin–Huxley model and the computational efficiency of integrate-and-fire neurons. As initiated by Bard Ermentrout and Nancy Kopell , this model is made of an oscillator producing slow oscillations combined with a switching mechanism for reproducing the bursting phenomenon . (...)
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<a href="http://atomosyd.net/spip.php/overlib/spip.php?rubrique36" rel="directory">Biological models</a>